Existence of Rayleigh resonances exponentially close to the real axis

G. Vodev

Annales de l'I.H.P. Physique théorique (1997)

  • Volume: 67, Issue: 1, page 41-57
  • ISSN: 0246-0211

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Vodev, G.. "Existence of Rayleigh resonances exponentially close to the real axis." Annales de l'I.H.P. Physique théorique 67.1 (1997): 41-57. <http://eudml.org/doc/76761>.

@article{Vodev1997,
author = {Vodev, G.},
journal = {Annales de l'I.H.P. Physique théorique},
keywords = {Neumann problem; elasticity operator; meromorphic continuation of the resolvent},
language = {eng},
number = {1},
pages = {41-57},
publisher = {Gauthier-Villars},
title = {Existence of Rayleigh resonances exponentially close to the real axis},
url = {http://eudml.org/doc/76761},
volume = {67},
year = {1997},
}

TY - JOUR
AU - Vodev, G.
TI - Existence of Rayleigh resonances exponentially close to the real axis
JO - Annales de l'I.H.P. Physique théorique
PY - 1997
PB - Gauthier-Villars
VL - 67
IS - 1
SP - 41
EP - 57
LA - eng
KW - Neumann problem; elasticity operator; meromorphic continuation of the resolvent
UR - http://eudml.org/doc/76761
ER -

References

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  1. [1] M. Kawashita, On the local-energy decay property for the elastic wave equation with the Neumann boundary conditions, Duke Math. J., Vol. 67, 1992, pp. 333-351. Zbl0795.35061MR1177309
  2. [2] M. Kawashita, On a region free from the poles of the resolvent and decay rate of the local energy for the elastic wave equation, Indiana Univ. Math. J., Vol. 43, 1994, pp. 1013-1043. Zbl0832.35088MR1305958
  3. [3] J. Sjöstrand, Singularités analytiques microlocales, Astérisque, Vol. 95, 1982. Zbl0524.35007MR699623
  4. [4] J. Sjöstrand and G. Vodev, Asymptotics of the number of Rayleigh resonances, Math. Ann., to appear. Zbl0890.35098MR1474193
  5. [5] P. Stefanov and G. Vodev, Distribution of resonances for the Neumann problem in linear elasticity outside a ball, Ann. Inst. H.Poincaré (Physique Théorique), Vol. 60, 1994, pp. 303-321. Zbl0805.73016MR1281649
  6. [6] P. Stefanov and G. Vodev, Distribution of resonances for the Neumann problem in linear elasticity outside a strictly convex body, Duke Math. J., Vol. 78, 1995, pp. 677-714. Zbl0846.35139MR1334206
  7. [7] P. Stefanov and G. Vodev, Neumann resonances in linear elasticity for an arbitrary body, Commun. Math. Phys., Vol. 176, 1996, pp. 645-659. Zbl0851.35032MR1376435
  8. [8] M. Taylor, Rayleigh waves in linear elasticity as a propagation of singularities phenomenon, in Proc. Conf. on P.D.E. and Geometry, Marcel Dekker, New York, 1979, pp. 273-291. Zbl0432.73021MR535598
  9. [9] G. Vodev, Sharp bounds on the number of scattering poles for perturbations of the Laplacian, Commun. Math. Phys., Vol. 146, 1992, pp. 205-216. Zbl0766.35032MR1163673
  10. [10] H. Walker, Some remarks on the local energy decay of solutions of the initial-boundary value problem for the wave equation in unbounded domains, J. Diff. Equations, Vol. 23, 1977, pp. 459-471. Zbl0337.35046MR427797
  11. [11] K. Yamamoto, Singularities of solutions to the boundary value problems for elastic and Maxwell's equations, Japan J. Math., Vol. 14, 1988, pp. 119-163. Zbl0669.73017MR945621

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